Sec 3 E-Math Trigonometry topical questions

A right-angled triangle has legs 9 cm and 12 cm. Find the hypotenuse.

Determine whether a triangle with sides 7, 24 and 25 is right-angled, showing your reasoning.

In a right triangle, the side opposite angle θ is 5 and the hypotenuse is 13. Write down sin θ and cos θ (the adjacent side is 12).

In a right triangle the side opposite θ is 4 and the side adjacent to θ is 7. Find θ, correct to 1 decimal place.

A right triangle has hypotenuse 10 and an angle of 35°. Find the side opposite the angle and the side adjacent to it, each correct to 3 significant figures.

A right-angled triangle has legs of 10 cm and 24 cm. (a) Find the hypotenuse. (b) Find both acute angles, correct to 1 decimal place.

1. (a)Hypotenuse.[1]
2. (b)Both acute angles.[2]

For an acute angle θ, sin θ = cos 62°. Find θ.

Find the area of a triangle with sides 9 cm and 7 cm enclosing an angle of 44°.

In triangle ABC, A = 52°, a = 8 cm and B = 70°. Find side b, correct to 3 significant figures.

In triangle ABC, a = 6 cm, b = 9 cm and C = 62°. Find side c, correct to 3 significant figures.

A triangle has sides 8 cm, 11 cm and 13 cm. Find the largest angle, correct to 1 decimal place.

A tower of height 45 m stands on level ground. From a point P the angle of elevation of the top is 32°. (a) Find the distance of P from the foot of the tower. (b) A second point Q is 60 m from the tower. Find the angle of elevation from Q.

1. (a)Distance of P.[3]
2. (b)Elevation from Q.[2]

A kite string is 85 m long and makes an angle of 52° with the horizontal ground. (a) Find the height of the kite. (b) Find its horizontal distance from the holder. (c) The string is then shortened to 60 m, keeping the same angle. Find the new height. (All answers to 3 significant figures.)

In triangle ABC, AB = 11 cm, BC = 14 cm and angle ABC = 78°. Find (a) the length AC, correct to 3 significant figures, and (b) the area of the triangle, correct to 3 significant figures.

A ship sails 40 km on a bearing of 048°, then 55 km on a bearing of 128°. (a) Show that the angle between the two legs of the journey is 100°. (b) Find the ship’s distance from its starting point. (c) Find the bearing of the ship from its starting point, correct to 1 decimal place.

1. (a)Angle between the legs.[2]
2. (b)Distance from the start.[2]
3. (c)Bearing from the start.[2]

From the top of an 80 m cliff, the angles of depression of two boats due east of the observer are 25° and 40°. (a) Find the distance of each boat from the foot of the cliff. (b) Find the distance between the boats.

1. (a)Distances of both boats.[3]
2. (b)Distance between the boats.[2]

A cuboid has edges AB = 8 cm, BC = 6 cm and CG = 4 cm (G is vertically above C). (a) Find the length of the base diagonal AC. (b) Find the space diagonal AG, correct to 3 significant figures. (c) Find the angle between AG and the base plane ABCD, correct to 1 decimal place.

1. (a)AC.[2]
2. (b)AG.[2]
3. (c)Angle with the base.[2]

In triangle ABC, a = 5 cm, b = 7 cm and C = 48°. (a) Find c. (b) Find angle A. (c) Find the area of the triangle.

1. (a)Side c.[2]
2. (b)Angle A.[2]
3. (c)Area.[2]

Two ships leave port P at the same time. Ship A sails 45 km on a bearing of 065°; ship B sails 35 km on a bearing of 155°. (a) Explain why angle APB = 90°. (b) Find the distance between the ships. (c) Find the bearing of B from A, correct to the nearest degree.

1. (a)Explain the right angle.[2]
2. (b)Distance between the ships.[2]
3. (c)Bearing of B from A.[2]

From a point A on level ground, the angle of elevation of the top of a tower is 48°. From a point B, 20 m closer to the tower and in line with A, the angle of elevation is 62°. Find the height of the tower, correct to 3 significant figures.